CN107704953A - The short-term wind-electricity power probability density Forecasting Methodology of EWT quantile estimate forests - Google Patents

The short-term wind-electricity power probability density Forecasting Methodology of EWT quantile estimate forests Download PDF

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CN107704953A
CN107704953A CN201710850654.7A CN201710850654A CN107704953A CN 107704953 A CN107704953 A CN 107704953A CN 201710850654 A CN201710850654 A CN 201710850654A CN 107704953 A CN107704953 A CN 107704953A
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孙国强
梁智
卫志农
臧海祥
周亦洲
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Hohai University HHU
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Abstract

The present invention discloses a kind of short-term wind-electricity power probability density Forecasting Methodology of EWT quantile estimates forest, comprises the following steps：1) original wind power sequence is decomposed into by series of features inequality empirical mode using experience wavelet transformation (empirical wavelet transform, EWT)；2) empirical mode is reconfigured according to frequency range, forms high frequency, intermediate frequency and low frequency component；3) input variable is chosen using Pearson correlation coefficients to each component；4) quantile estimate forest forecast model is established to each component, obtains different quantile regression forecasting results；5) each component prediction result is superimposed, obtains wind power prediction value；6) prediction of wind power probability density is obtained using Density Estimator.The method provided by the present invention effectively increases wind power prediction precision, obtains the prediction of any time wind power probability density, can preferably solve the problems, such as power system wind power prediction.

Description

The short-term wind-electricity power probability density Forecasting Methodology of EWT quantile estimate forests
Technical field
The present invention relates to a kind of power-system short-term wind power probability density Forecasting Methodology, to power system wind power It is predicted, belongs to technical field of power systems.
Background technology
Wind-power electricity generation is installed the rising year by year of ratio in power network, effectively alleviates energy shortage, environmental pollution general layout, but Its intermittent and uncertain safety and stability and economical operation that drastically influence power network again.Short-term wind-electricity power prediction is as certainly Dynamic Generation Control and the important decision foundation for arranging power scheduling, can effectively improve Operation of Electric Systems reliability.Therefore, need New technology and new method are studied, to improve wind power prediction precision, meets engineer applied demand.
At present, domestic and foreign scholars have carried out numerous studies, main having time sequence analysis, people to short-term wind-electricity power prediction The models such as artificial neural networks, SVMs, Method Using Relevance Vector Machine.In addition, further to reduce wind power prediction error, it is related Scholar proposes combination forecasting.It facts have proved：Built-up pattern can have complementary advantages relative to Individual forecast method, improve While precision of prediction, model robustness is enhanced.Combined prediction is different by mechanism strategy, is broadly divided into two classes：1) using not Forecast model with principle is predicted respectively, and prediction result then is optimized into combination by certain way；2) signal is used Treatment technology carries out resolution process to original wind power sequence, forecast model is established to different decomposition amount, finally to each component Prediction result is combined.Using wavelet transformation progress, data prediction is faced with wavelet basis selection, Decomposition order is difficult to The problem of determining.Wind power sequence is automatically decomposed into by a series of intrinsic mode letters using adaptive empirical mode decomposition , when then establishing forecast model to mode function, modal overlap phenomenon be present, influence precision of prediction in number.Integrated empirical modal point Solution method effectively alleviates modal overlap problem existing for empirical mode decomposition, improves precision of prediction, but its amount of calculation it is larger, Operation efficiency is low.
Easily occur the shortcomings of low modal overlap, computational efficiency, shortage theoretical foundation for empirical mode decomposition method, Gilles propose NEW ADAPTIVE signal processing method-experience wavelet transformation (empirical wavelet transform, EWT).This method combines the adaptive characteristic and Wavelet Analysis Theory framework of empirical mode decomposition method, by signal frequency The adaptivenon-uniform sampling of spectrum, the amplitude modulationfrequency modulation of Fourier spectrum is extracted in the suitable orthogonal wavelet filter of each spectrum architecture (amplitude modulated-frequencymodulated, AM-FM) composition, and then converted using Hilbert to difference AM-FM mode handled, finally obtain significant instantaneous frequency and instantaneous amplitude.This method amount of calculation is small, and has Stronger robustness.Therefore, EWT is introduced into short-term wind-electricity power prediction modeling by the present invention, and original wind power sequence is entered Row resolution process.
In general short-term wind power forecast method only provides deterministic point prediction as a result, it is difficult to which wind energy is fully described Uncertainty and changing rule, so as to be unfavorable for policymaker in Electric Power Network Planning operation, risk analysis, reliability assessment etc. Make scientific and effective decision-making.Therefore, related scholar proposes short-term wind-electricity power probability forecasting method, as quantile estimate, Interval prediction, density prediction etc..Probabilistic forecasting can preferably describe the possible fluctuation range of following wind power, uncertainty And the risk faced.Nicolai combinations quantile estimate is theoretical, is proposed on the basis of random forest (random forest, RF) Quantile estimate forest (quantile regression forests, QRF) model, different quantiles can be provided and returned Prediction result.As a kind of nonparametric ensemble machine learning method, QRF has that arithmetic speed is fast, model performance is influenceed by parameter concurrently Small, relatively strong the advantages that holding making an uproar property.The present invention establishes QRF wind power prediction models, is obtaining different quantile prediction output bars Under part, the prediction of wind power probability density is further obtained using Density Estimator.
In summary, the present invention combines EWT and QRF advantages, establishes EWT-QRF short-term wind-electricity powers probability density prediction mould Type.First, original wind power sequence is decomposed into by a series of different empirical mode of frequencies using EWT, to each Empirical Mode Formula establishes QRF forecast models respectively, obtains different quantile regression forecasting results, and each empirical mode prediction result is superimposed, obtained To final wind power prediction value.Finally, the prediction of wind power probability density is provided using Density Estimator method.
The content of the invention
Goal of the invention：The present invention is for problem present in existing Load Prediction In Power Systems technology, such as in general wind-powered electricity generation Power forecasting method can only export deterministic point prediction as a result, it is difficult to reflect randomness, the uncertainty of wind power completely Easily there is the problems such as low modal overlap, computational efficiency, shortage theoretical foundation shortcoming in feature, empirical mode decomposition method, there is provided one The short-term wind-electricity power probability density Forecasting Methodology of kind EWT quantile estimate forests.The present invention uses EWT by original wind-powered electricity generation first Power sequence is decomposed into the empirical mode of series of features inequality, and choosing input variable collection to each empirical mode merges foundation point Digit returns forest forecast model, obtains the prediction result under the conditions of any quantile.Predicted by being superimposed different empirical modes As a result, final short-term wind-electricity power predicted value is obtained.Finally, the condition distribution to predicted value is obtained using Density Estimator method Obtain any time wind power probability density prediction result.
Technical scheme：A kind of short-term wind-electricity power probability density Forecasting Methodology of EWT quantile estimates forest, including it is following Step：
(1) master data needed for power system short-term wind power prediction is obtained, and initial data is pre-processed, Carry out abnormality value removing or amendment；
(2) pretreated wind power sequence is decomposed into the empirical mode of series of features inequality using EWT；
(3) empirical mode is reconfigured according to frequency range, forms high fdrequency component, intermediate frequency component and low frequency point Amount；
(4) input variable set is chosen using Pearson correlation coefficients to each component；
(5) quantile estimate forest model is established to each component, obtains different quantile regression forecasting results；
(6) each component prediction result is superimposed, obtains final wind power prediction value；
(7) prediction of wind power probability density is obtained using Density Estimator, and by surveying wind power data verification The validity of the inventive method.
Further, original wind power sequence is decomposed into a series of frequecy characteristic inequalities by step (2) using EWT technologies Empirical mode, the specific calculating process of EWT methods is：
2.1 determine the frequency range of bandpass filter；Adaptivenon-uniform sampling, definition are carried out to the Fourier spectrums of signal first Fourier supports is [0, π] and assume to be divided into N number of continuous part, make Λn=[wn-1,wn] represent each segmentation side Boundary；Wherein：N=1,2, L, N, w0=0, wN=π, wnIn being chosen between the two neighboring maximum point of signal Fourier spectrums Point, it is obvious
2.2 with each wnCentered on, definition width is Tn=2 τnTransitional region；
2.3 in segmentation section ΛnOn, it is each Λ to define experience small echonOn bandpass filter, and according to Meyer small echos Building method constructs experience small echo, and the experience wavelet function generally constructed is
Experience scaling function is
In formula：τn=γ wn；When, it ensure thatFor tight frame；Generally, letter Number β (x) is defined as β (x)=x4(35-84x+70x2-20x3)；
2.4 so as to which primary signal can be reconfigured as
In formula：* it is convolution algorithm；For Coefficients of Approximation；For x (t) experience wavelet transformation；
Empirical mode xk(t) it is defined as
Further, step (3) is reconfigured empirical mode according to frequency range, forms high fdrequency component, intermediate frequency Component and low frequency component, the frequency range demarcation method are specially：Empirical mode in [0, π] frequency range is divided into three Part：Frequency being more than 1 for low frequency component, frequency and being more than 2 as high frequency division less than 2 for intermediate frequency component, frequency less than 1 Amount.
Further, step (4) chooses input variable set, the Pearson to each component using Pearson correlation coefficients Coefficient correlation circular is：
Preset time sequence, Pearson correlation coefficients have weighed xtWith xt-τBetween dependency relation, can effectively determine defeated Enter variables collection；Wherein, τ is lag order；Pearson correlation coefficients r spans are [- 1,1], and 1 represents perfect positive correlation ,- 1 represents perfect negative correlation, and 0 represents non-correlation between variable；When | r | during ＞ 0.3, that is, think exist between variable compared with strong correlation pass System；Coefficient correlation calculation formula is between moment wind power to be predicted and preceding τ moment power
In formula：xt,i、xt-τ,iRespectively variable xtAnd xt-τI-th of sample value；Respectively variable xtAnd xt-τ's Average value；N is sample size.
Further, step (5) establishes quantile estimate forest model to each component, obtains different quantile regression forecastings As a result；Quantile estimate forest model combines the advantage of quantile estimate and Random Forest model, can provide difference point position Point regression forecasting result；As a kind of nonparametric ensemble machine learning method, QRF has that arithmetic speed is fast, model performance is joined concurrently Number influences small, relatively strong the advantages that holding making an uproar property；The specific calculating process of quantile estimate is：
5.1 under specified criteria X=x, and conditional distribution function is Y≤y cumulative probability, i.e.,
F (y | X=x)=P (Y≤y | X=x)
α quantiles Qα(x) it is that Y is more than or equal to Q under the conditions of given X=xα(x) cumulative probability is exactly α, i.e.,
Qα(x)=inf { y:F (y | X=x) >=α }
5.2 in general linear conditions quantile estimates are expressed as
QY(α | X=x)=β0(α)+β1(α)x1+β2(α)x2+L+βk(α)xk≡X′β(α)
In formula：QY(α | X=x) is dependent variable Y in independent variable X=[x1,x2,L,xk] under the α condition quantile, point Site α ∈ (0,1), β (α) is regression coefficient vector, and it changes with quantile α change；
5.3 condition quantiles solve parameter vector β (α) estimate by minimizing loss function, define loss function For
5.4 can be converted into following optimization problem so as to quantile estimate
Give some quantile α, pass through parameter vector estimate corresponding to solution, you can describe independent variable now to because The influence of variable；Then when α is in the continuous value in (0,1) feasible section, you can obtain Y condition distribution.
Further, step (5) establishes quantile estimate forest model to each component, obtains different quantile regression forecastings As a result；The specific calculating process of quantile estimate forest is：
6.1 random forests are counted as an adaptability nearest neighbour classification and regression process, to each X=x, can obtain Original one weight set w of n observed valuei(x), i=1,2, L, n；Random forest essence is to utilize all dependent variable observations Estimation of the weighted sum as dependent variable Y conditional means E (Y | X=x)；In addition, QRF decision trees are produced with standard RF algorithms, Condition distribution is obtained by the dependent variable Weighted estimation observed, wherein the weight of each observation is equal to RF algorithm weights；
6.2 thus, QRF defines E (1{Y≤y}| X=x) be estimated as observation 1{Y≤y}Weighted average, i.e.,
6.3 k decision tree T (θ of generationt), t=1,2, L, k；To each leaf node of every decision tree, the leaf node is investigated All observations；
6.4 given X=x, travel through all decision trees；Calculate the weight w of every decision tree observationi(x,θt), i ∈ 1,2, L,n}；By to decision tree weight wi(x,θt), t=1,2, L, k are averaged to obtain the weight of each observation i ∈ { 1,2, L, n } wi(x)；
6.5 couples of all y ∈ R, the weight drawn using step 6.4, you can calculate the estimation of distribution function；To every decision-making Each node of tree, RF, which is returned, only to be retained the average of observation and have ignored other information, and QRF retains all observations in node Value, and condition distribution is calculated on this basis.
Further, the prediction of wind power probability density is obtained using Density Estimator in step (7), and by surveying wind The validity of electrical power data verification the inventive method；The specific calculating process of Density Estimator is：
Density Estimator is to estimate its density by the stochastic variable from same unknown distribution function of one group of observation The nonparametric computational methods of function；If X1,X2,L,XnIt is taken from unitary continuous population sample, the total body density at the x of arbitrfary point Function f (x) Density Estimator is defined as
In formula：K (x) is kernel function, the gaussian kernel function form used herein forH is bandwidth Coefficient, span are 1.8~2.0.
Beneficial effect：The power-system short-term wind power probability density Forecasting Methodology of the present invention utilizes EWT by original wind Electrical power sequence is decomposed into the empirical mode of series of features inequality, and input variable is chosen to each empirical mode and is established and divides position Number returns forest forecast model, obtains the regression forecasting result under the conditions of any quantile, further obtains wind power probability Density prediction.Relative in general Forecasting Methodology, the inventive method can provide the prediction of any time wind power probability density As a result, scientific and effective determine is made in Electric Power Network Planning operation, risk analysis, reliability assessment etc. so as to be beneficial to policymaker Plan.
Brief description of the drawings
Fig. 1 is split for Fourier spectrum；
Fig. 2 is original wind power sequence and EWT decomposition results；
Fig. 3 is empirical mode spectrum distribution；
Fig. 4 is empirical mode reconstruction result；
Fig. 5 is original wind power sequence and EMD decomposition results；
Fig. 6 is that EMD decomposes mode function reconstruct component；
Fig. 7 is 80% confidential interval probabilistic forecasting result；
Fig. 8 is 1:00 moment probability density is predicted；
Fig. 9 is 5:00 moment probability density is predicted；
Figure 10 is 9:00 moment probability density is predicted；
Figure 11 is 13:00 moment probability density is predicted；
Figure 12 is 17:00 moment probability density is predicted；
Figure 13 is 21:00 moment probability density is predicted.
Embodiment
With reference to specific embodiment, the present invention is furture elucidated, it should be understood that these embodiments are merely to illustrate the present invention Rather than limitation the scope of the present invention, after the present invention has been read, various equivalences of the those skilled in the art to the present invention The modification of form falls within the application appended claims limited range.
To effectively improve short-term wind-electricity power precision of prediction, the inventive method is carried out pre- using EWT to original wind power Processing, is broken down into the empirical mode of series of features inequality, forecast model is established to each empirical mode.Experience small echo sheet It is the one group of bandpass filter selected according to signal spectrum characteristic in matter, so as to adaptively filter out tune from primary signal Width-frequency modulation composition.In order to determine the frequency range of bandpass filter, adaptivenon-uniform sampling is carried out to the Fourier spectrums of signal first.
Illustrate EWT adaptive decomposition processes with reference to Fig. 1.According to Shannon criterion, Fourier supports are defined as [0, π] and vacation Surely N number of continuous part is divided into, makes Λn=[wn-1,wn] represent each segmentation border.Wherein：N=1,2, L, N, w0= 0,wN=π, wnThe midpoint being chosen between the two neighboring maximum point of signal Fourier spectrums, it is obviousWith every Individual wnCentered on, definition width is Tn=2 τnTransitional region, as shown in dash area in figure.In segmentation section ΛnOn, definition Experience small echo is each ΛnOn bandpass filter, and according to Meyer wavelet construction methods construct experience small echo.Gilles structures The experience wavelet function made is
Experience scaling function is
In formula：τn=γ wn；When, it ensure thatFor tight frame.Generally, letter Number β (x) is defined as β (x)=x4(35-84x+70x2-20x3)。
So as to which primary signal can be reconfigured as
In formula：* it is convolution algorithm；For Coefficients of Approximation；For x (t) experience wavelet transformation.
Empirical mode xk(t) define as the following formula
Standard regression analysis is under the conditions of given X=x, and dependent variable Y is obtained by minimizing square error loss function Conditional mean E (Y | X=x) estimation, but this method can only provide the one-sided information of dependent variable Y conditions distribution, have ignored it His information.In addition, when Y is when being distributed as containing singular value in thick tail or data, Regression Analysis Result robustness is poor.And divide Digit recurrence is that dependent variable Y condition quantile returns to independent variable X, so as to obtain all quantile Regressions prediction moulds Type.Therefore, quantile estimate more can accurately describe changes of the independent variable X to dependent variable Y relative to common least square regression The influence of scope and condition distribution shape.
Under specified criteria X=x, conditional distribution function is Y≤y cumulative probability, i.e.,
F (y | X=x)=P (Y≤y | X=x) (5)
α quantiles Qα(x) it is that Y is more than or equal to Q under the conditions of given X=xα(x) cumulative probability is exactly α, i.e.,
Qα(x)=inf { y:F (y | X=x) >=α } (6)
In general linear conditions quantile estimate is expressed as
QY(α | X=x)=β0(α)+β1(α)x1+β2(α)x2+L+βk(α)xk≡X′β(α) (7)
In formula：QY(α | X=x) is dependent variable Y in independent variable X=[x1,x2,L,xk] under the α condition quantile, quantile α ∈ (0,1), β (α) is regression coefficient vector, and it changes with quantile α change.
Condition quantile solves parameter vector β (α) estimate by minimizing loss function, defines loss function and is
So as to which quantile estimate can be converted into following optimization problem
Give some quantile α, pass through parameter vector estimate corresponding to solution, you can describe independent variable now to because The influence of variable.Then when α is in the continuous value in (0,1) feasible section, you can obtain Y condition distribution.
QRF is the innovatory algorithm of Breiman random forests, by combine quantile estimate characteristic, so as to provide because The full terms distributed intelligence of variable.QRF possesses theoretical foundation, is proved to simultaneously as a kind of nonparametric machine learning method With uniformity.
RF is counted as an adaptability nearest neighbour classification and regression process, to each X=x, can obtain original n sight Examine one weight set w of valuei(x), i=1,2, L, n.RF essence is the weighted sum by the use of all dependent variable observations as because becoming Measure Y conditional means E (Y | X=x) estimation.In addition, QRF decision trees are produced with standard RF algorithms, condition distribution is to pass through sight The dependent variable Weighted estimation measured obtains, wherein the weight of each observation is equal to RF algorithm weights.
Thus, QRF defines E (1{Y≤y}| X=x) be estimated as observation 1{Y≤y}Weighted average, i.e.,
QRF algorithms concretely comprise the following steps：
1) k decision tree T (θ is generatedt), t=1,2, L, k.To each leaf node of every decision tree, the leaf node institute is investigated There is observation；
2) X=x is given, travels through all decision trees.Calculate the weight w of every decision tree observationi(x,θt), i ∈ 1,2, L,n}.By to decision tree weight wi(x,θt), t=1,2, L, k are averaged to obtain the weight of each observation i ∈ { 1,2, L, n } wi(x)；
3) to all y ∈ R, the weight drawn using step 2), the estimation of distribution function is calculated by formula (10).
To each node of every decision tree, RF, which is returned, only to be retained the average of observation and have ignored other information, and QRF Retain all observations in node, and calculate condition distribution on this basis.
The present invention obtains probability density prediction result using Density Estimator method from condition distribution.Density Estimator is The nonparametric computational methods of its density function are estimated by the stochastic variable from same unknown distribution function of one group of observation. If X1,X2,L,XnUnitary continuous population sample is taken from, the Density Estimator of the population density function f (x) at the x of arbitrfary point is determined Justice is
In formula：K (x) is kernel function, the gaussian kernel function form that uses of the present invention forH is band Wide coefficient, span are 1.8~2.0.
The shortcomings that being difficult to characterize changed power uncertainty completely for general wind power point prediction method, the present invention is built EWT-QRF short-term wind-electricity power probability density forecast models have been found, any time wind power fluctuation range and general can be obtained Rate density exports.First, original wind power sequence is pre-processed using EWT signal processing technologies, by its adaptive point Solve as the empirical mode of some frequency inequalities.Task amount is modeled to reduce, empirical mode similar in frequency size is merged into newly Component.Secondly, the merging of input variable collection is chosen to new component and establishes QRF forecast models, obtain the wind under different quantiles Electrical power prediction result, and different component prediction results are superimposed to the condition distribution for obtaining predicted value.Finally, estimated using cuclear density The output wind power probability density prediction of meter method.
Using wind power plant actual measurement wind power data as research object, the inventive method estimated performance is verified.Datum It is 30min according to sampling time interval, original wind power sequence is decomposed using EWT methods, selected part result such as Fig. 2 It is shown.It can be seen that original wind power is decomposed into 11 empirical modes by EWT, each mode frequency feature is more Substantially.Fig. 3 is each mode spectrum section boundaries value, and empirical mode is divided into three classes by the present invention according to frequency size, is respectively Low frequency, intermediate frequency and high frequency, then merge the empirical mode in class, are reconstructed into low frequency component, intermediate frequency component and height respectively Frequency component.QRF forecast models are established to each component, so as to reduce modeling work amount, improve efficiency.Fig. 4 reconstructs for each component As a result.
To illustrate that EWT is used for the validity of wind power prediction, EMD methods are used for point of power data by the present invention simultaneously Solution, and contrast prediction result.Fig. 5 and Fig. 6 is respectively EMD decomposition results and reconstruct component.
The selection of input variable has to model prediction performance to be directly affected, and the present invention is quantified using Pearson correlation coefficients The correlation between variable is evaluated, and the larger input variable set of correlation is chosen from preceding 10 moment at moment to be predicted. Preset time sequence, Pearson correlation coefficients have weighed xtWith xt-τBetween dependency relation, can effectively determine input variable collection Close.Wherein, τ is lag order.Pearson correlation coefficients r spans are [- 1,1], and 1 represents perfect positive correlation, and -1 has represented Complete negatively correlated, 0 represents non-correlation between variable.When | r | during ＞ 0.3, that is, think exist between variable compared with strong correlation relation.It is to be predicted Coefficient correlation calculation formula is between moment wind power and preceding τ moment power
In formula：xt,i、xt-τ,iRespectively variable xtAnd xt-τI-th of sample value；Respectively variable xtAnd xt-τ's Average value；N is sample size.
Input variable set is chosen to the component that EWT and EMD is decomposed, as a result respectively as shown in Table 1 and Table 2.
Table 1EWT component Input variable selection results
Table 2EMD component Input variable selection results
Missed using mean absolute percentage error (mean absolute percentage error, MAPE) and root mean square Poor (root mean square error, RMSE) is used as certainty point prediction modelling effect evaluation index, calculation formula difference For
In formula：N is future position number；yi、Respectively i-th of future position power actual value and predicted value.
Using section coverage rate (interval coverage percentage, ICP) and section mean breadth (interval average width, IAW) is used as probability interval forecast model evaluation index, and calculation formula is respectively
In formula：ξ1-αFor under given 1- α level of confidence real power value fall the number in confidential interval；uiFor i-th The individual future position confidential interval upper limit, liFor i-th of future position lower limit of confidence interval.
30min predictions, and verify the inventive method estimated performance in advance are carried out to actual measurement wind power.
1) directly original power data are predicted.Quantile estimate forest parameters are arranged to：Decision tree number is 500, node minimum dimension is 5, and every decision tree randomly selects m from input variable settry=2M/3 variable carries out weight Study, M choose with reference to table 1.To obtain condition distribution, it is 0.01~0.99 that the present invention, which sets quantile scope, step-length 0.01, 99 prediction results can be obtained to each future position.Meanwhile the present invention establishes BP, SVMs (support Vector machines, SVM) contrast model.BP learning rates are 0.001, learning objective 0.01, iteration 10000 times, model Structural parameters through test of many times relatively after be arranged to 9-15-1, wherein first parameter is input layer variable number, hidden layer god It is 15 through first number, output layer neuron number is 1.SVM model learnings parameter C and ε passes through grid data service optimum option, ginseng Number scopes are [- 8,8], iteration step length 1.Table 3 is BP, SVM and QRF model prediction result, and QRF models take 0.5 quantile bar Predicted value under part.As can be seen that during using Individual forecast model, predicted value lags behind actual value variation tendency, hysteresis be present, Cause larger prediction error.
2) EMD and EWT methods are respectively adopted resolution process is carried out to original power data, then each component is built respectively Vertical forecast model.Built-up pattern effectively increases precision of prediction as can be seen from Table 3.In addition, EWT method performances are better than EMD methods, EWT-BP, EWT-SVM, EWT-QRF are carried respectively relative to EMD-BP, EMD-SVM, EMD-QRF model M APE indexs High 24.97%, 13.58% and 22.07%, RMSE index be respectively increased 27.20%, 19.37% and 29.63%.Wherein： EMD-BP models random component, details coefficients and trend component structural parameters are followed successively by 4-11-1,8-16-1 and 10-17-1, EWT-BP models high fdrequency component, intermediate frequency component and low frequency component structural parameters are followed successively by 5-9-1,7-15-1 and 10-15-1；SVM With QRF parameter settings with 1).Fig. 7 is power interval prediction result under 80% confidence level, and EWT-QRF interval widths are narrower, excellent Gesture is obvious, so as to be more beneficial for science decision.
The different model wind power prediction result statistics of table 3
The condition distribution obtained to QRF, EMD-QRF and EWT-QRF can provide any time wind using Density Estimator Electrical power probability density prediction result, choose one day at different moments prediction result as shown in Fig. 8-Figure 13.As can be seen that EWT- For QRF models with high probability close to actual value, probability density curve is taller and thinner, and fluctuation range is more concentrated, and is advantageous in narrower model Educated decisions are made in enclosing.
In summary, the short-term wind-electricity power probability density Forecasting Methodology of a kind of EWT quantile estimates forest of the invention With following advantage：1) using EWT, this NEW ADAPTIVE signal processing method is carried out at decomposition to original wind power sequence Reason, it is broken down into the empirical mode of multiple frequecy characteristic inequalities.Relative to EMD methods, the component that EWT is decomposed is with more explanation Meaning.Secondly, the EWT-QRF forecast models of foundation have more preferable precision of prediction relative to EMD-QRF models, and MAPE indexs carry High 29.31%, RMSE indexs improve 29.63%.Under same confidence level, interval width is narrower, is advantageous to make determining for science Plan.2) quantile estimate forest model can provide the prediction result under any quantile, so as to obtain the distribution of predicted value condition, And further obtain the prediction of wind power probability density.Quantile estimate forest as a kind of Nonparametric Estimation, have by Model parameter influences the advantages of small, strong robustness, less amount of calculation, is suitably applied the prediction of short-term wind-electricity power probability density.
The inventive method arranges power system wind-powered electricity generation, and operation plan and guarantee power network safety operation have one a few days ago Fixed reference value.

Claims (7)

  1. A kind of 1. short-term wind-electricity power probability density Forecasting Methodology of EWT quantile estimates forest, it is characterised in that：Including following Step：
    (1) master data needed for power system short-term wind power prediction is obtained, and initial data is pre-processed, is carried out Abnormality value removing or amendment；
    (2) pretreated wind power sequence is decomposed into the empirical mode of series of features inequality using EWT；
    (3) empirical mode is reconfigured according to frequency range, forms high fdrequency component, intermediate frequency component and low frequency component；
    (4) input variable set is chosen using Pearson correlation coefficients to each component；
    (5) quantile estimate forest model is established to each component, obtains different quantile regression forecasting results；
    (6) each component prediction result is superimposed, obtains final wind power prediction value；
    (7) prediction of wind power probability density is obtained using Density Estimator, and by surveying wind power data verification this hair The validity of bright method.
  2. 2. the short-term wind-electricity power probability density Forecasting Methodology of EWT quantile estimates forest according to claim 1, it is special Sign is：Original wind power sequence is decomposed into a series of Empirical Mode of frequecy characteristic inequalities using EWT technologies by step (2) Formula, the specific calculating process of EWT methods are：
    2.1 determine the frequency range of bandpass filter；Adaptivenon-uniform sampling, definition are carried out to the Fourier spectrums of signal first Fourier supports is [0, π] and assume to be divided into N number of continuous part, make Λn=[wn-1,wn] represent each segmentation side Boundary；Wherein：N=1,2, L, N, w0=0, wN=π, wnIn being chosen between the two neighboring maximum point of signal Fourier spectrums Point, it is obvious
    2.2 with each wnCentered on, definition width is Tn=2 τnTransitional region；
    2.3 in segmentation section ΛnOn, it is each Λ to define experience small echonOn bandpass filter, and according to Meyer Construction of Wavelets Method construct experience small echo, the experience wavelet function generally constructed are
    <mrow> <msub> <mover> <mi>&amp;psi;</mi> <mo>^</mo> </mover> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>w</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <msub> <mi>w</mi> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>&amp;tau;</mi> <mi>n</mi> </msub> <mo>&amp;le;</mo> <mrow> <mo>|</mo> <mi>w</mi> <mo>|</mo> </mrow> <mo>&amp;le;</mo> <msub> <mi>w</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>cos</mi> <mo>&amp;lsqb;</mo> <mfrac> <mi>&amp;pi;</mi> <mn>2</mn> </mfrac> <mi>&amp;beta;</mi> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>&amp;tau;</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mo>(</mo> <mrow> <mrow> <mo>|</mo> <mi>w</mi> <mo>|</mo> </mrow> <mo>-</mo> <msub> <mi>w</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>w</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;le;</mo> <mrow> <mo>|</mo> <mi>w</mi> <mo>|</mo> </mrow> <mo>&amp;le;</mo> <msub> <mi>w</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>sin</mi> <mo>&amp;lsqb;</mo> <mfrac> <mi>&amp;pi;</mi> <mn>2</mn> </mfrac> <mi>&amp;beta;</mi> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>&amp;tau;</mi> <mi>n</mi> </msub> </mrow> </mfrac> <mo>(</mo> <mrow> <mrow> <mo>|</mo> <mi>w</mi> <mo>|</mo> </mrow> <mo>-</mo> <msub> <mi>w</mi> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>&amp;tau;</mi> <mi>n</mi> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>w</mi> <mi>n</mi> </msub> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mi>n</mi> </msub> <mo>&amp;le;</mo> <mrow> <mo>|</mo> <mi>w</mi> <mo>|</mo> </mrow> <mo>&amp;le;</mo> <msub> <mi>w</mi> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>&amp;tau;</mi> <mi>n</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>o</mi> <mi>t</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> <mi>w</mi> <mi>i</mi> <mi>s</mi> <mi>e</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
    Experience scaling function is
    <mrow> <msub> <mover> <mi>&amp;phi;</mi> <mo>^</mo> </mover> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>w</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <mrow> <mo>|</mo> <mi>w</mi> <mo>|</mo> </mrow> <mo>&amp;le;</mo> <msub> <mi>w</mi> <mi>n</mi> </msub> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mi>n</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mo>&amp;lsqb;</mo> <mfrac> <mi>&amp;pi;</mi> <mn>2</mn> </mfrac> <mi>&amp;beta;</mi> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>&amp;tau;</mi> <mi>n</mi> </msub> </mrow> </mfrac> <mo>(</mo> <mrow> <mrow> <mo>|</mo> <mi>w</mi> <mo>|</mo> </mrow> <mo>-</mo> <msub> <mi>w</mi> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>&amp;tau;</mi> <mi>n</mi> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>w</mi> <mi>n</mi> </msub> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mi>n</mi> </msub> <mo>&amp;le;</mo> <mrow> <mo>|</mo> <mi>w</mi> <mo>|</mo> </mrow> <mo>&amp;le;</mo> <msub> <mi>w</mi> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>&amp;tau;</mi> <mi>n</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>o</mi> <mi>t</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> <mi>w</mi> <mi>i</mi> <mi>s</mi> <mi>e</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
    In formula：τn=γ wn；When, it ensure thatFor tight frame；Generally, function β (x) it is defined as β (x)=x4(35-84x+70x2-20x3)；
    2.4 so as to which primary signal can be reconfigured as
    <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>W</mi> <mi>x</mi> <mi>&amp;epsiv;</mi> </msubsup> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>*</mo> <msub> <mi>&amp;phi;</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msubsup> <mi>W</mi> <mi>x</mi> <mi>&amp;epsiv;</mi> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>*</mo> <msub> <mi>&amp;phi;</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow>
    In formula：* it is convolution algorithm；For Coefficients of Approximation；For x (t) experience wavelet transformation；
    Empirical mode xk(t) it is defined as
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>=</mo> <msubsup> <mi>W</mi> <mi>x</mi> <mi>&amp;epsiv;</mi> </msubsup> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>t</mi> <mo>)</mo> <mo>*</mo> <msub> <mi>&amp;phi;</mi> <mn>1</mn> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>=</mo> <msubsup> <mi>W</mi> <mi>x</mi> <mi>&amp;epsiv;</mi> </msubsup> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> <mo>*</mo> <msub> <mi>&amp;phi;</mi> <mi>n</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow>
  3. 3. the short-term wind-electricity power probability density Forecasting Methodology of EWT quantile estimates forest according to claim 1, it is special Sign is：Step (3) is reconfigured empirical mode according to frequency range, forms high fdrequency component, intermediate frequency component and low frequency Component, the frequency range demarcation method are specially：Empirical mode in [0, π] frequency range is divided into three parts：Frequency It is low frequency component less than 1, frequency is more than 1 and is more than 2 as high fdrequency component less than 2 for intermediate frequency component, frequency.
  4. 4. the short-term wind-electricity power probability density Forecasting Methodology of EWT quantile estimates forest according to claim 1, it is special Sign is：Step (4) chooses input variable set, the Pearson correlation coefficients tool to each component using Pearson correlation coefficients Body computational methods are：
    Preset time sequence, Pearson correlation coefficients have weighed xtWith xt-τBetween dependency relation, can effectively determine input become Duration set；Wherein, τ is lag order；Pearson correlation coefficients r spans are [- 1,1], and 1 represents perfect positive correlation, -1 table Show perfect negative correlation, 0 represents non-correlation between variable；When | r | during ＞ 0.3, that is, think exist between variable compared with strong correlation relation；Treat Coefficient correlation calculation formula is between prediction time wind power and preceding τ moment power
    <mrow> <mi>r</mi> <mo>=</mo> <mfrac> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <msqrt> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>&amp;CenterDot;</mo> <msqrt> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow>
    In formula：xt,i、xt-τ,iRespectively variable xtAnd xt-τI-th of sample value；Respectively variable xtAnd xt-τBe averaged Value；N is sample size.
  5. 5. the short-term wind-electricity power probability density Forecasting Methodology of EWT quantile estimates forest according to claim 1, it is special Sign is：Step (5) establishes quantile estimate forest model to each component, obtains different quantile regression forecasting results；Divide position Number returns the advantage that forest model combines quantile estimate and Random Forest model, can provide different quantile regression forecastings As a result；As a kind of nonparametric ensemble machine learning method, QRF have concurrently arithmetic speed is fast, model performance by parameter influenceed it is small, compared with Strong the advantages that holding making an uproar property；The specific calculating process of quantile estimate is：
    5.1 under specified criteria X=x, and conditional distribution function is Y≤y cumulative probability, i.e.,
    F (y | X=x)=P (Y≤y | X=x)
    α quantiles Qα(x) it is that Y is more than or equal to Q under the conditions of given X=xα(x) cumulative probability is exactly α, i.e.,
    Qα(x)=inf { y:F (y | X=x) >=α }
    5.2 in general linear conditions quantile estimates are expressed as
    QY(α | X=x)=β0(α)+β1(α)x1+β2(α)x2+L+βk(α)xk≡X′β(α)
    In formula：QY(α | X=x) is dependent variable Y in independent variable X=[x1,x2,L,xk] under the α condition quantile, quantile α ∈ (0,1), β (α) is regression coefficient vector, and it changes with quantile α change；
    5.3 condition quantiles solve parameter vector β (α) estimate by minimizing loss function, define loss function and are
    <mrow> <msub> <mi>L</mi> <mi>&amp;alpha;</mi> </msub> <mrow> <mo>(</mo> <mi>y</mi> <mo>,</mo> <msup> <mi>X</mi> <mo>&amp;prime;</mo> </msup> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mi>&amp;alpha;</mi> <mrow> <mo>|</mo> <mrow> <mi>y</mi> <mo>-</mo> <msup> <mi>X</mi> <mo>&amp;prime;</mo> </msup> <mi>&amp;beta;</mi> </mrow> <mo>|</mo> </mrow> <mo>,</mo> <mi>y</mi> <mo>&gt;</mo> <msup> <mi>X</mi> <mo>&amp;prime;</mo> </msup> <mi>&amp;beta;</mi> </mtd> </mtr> <mtr> <mtd> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&amp;alpha;</mi> <mo>)</mo> <mrow> <mo>|</mo> <mrow> <mi>y</mi> <mo>-</mo> <msup> <mi>X</mi> <mo>&amp;prime;</mo> </msup> <mi>&amp;beta;</mi> </mrow> <mo>|</mo> </mrow> <mo>,</mo> <mi>y</mi> <mo>&amp;le;</mo> <msup> <mi>X</mi> <mo>&amp;prime;</mo> </msup> <mi>&amp;beta;</mi> </mtd> </mtr> </mtable> </mfenced> </mrow>
    5.4 can be converted into following optimization problem so as to quantile estimate
    <mrow> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mi>&amp;beta;</mi> </munder> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>|</mo> <msub> <mi>Y</mi> <mi>i</mi> </msub> <mo>&amp;GreaterEqual;</mo> <msubsup> <mi>X</mi> <mi>i</mi> <mo>&amp;prime;</mo> </msubsup> <mi>&amp;beta;</mi> </mrow> </munder> <mi>&amp;alpha;</mi> <mo>|</mo> <mrow> <msub> <mi>Y</mi> <mi>i</mi> </msub> <mo>-</mo> <msubsup> <mi>X</mi> <mi>i</mi> <mo>&amp;prime;</mo> </msubsup> <mi>&amp;beta;</mi> </mrow> <mo>|</mo> <mo>+</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>|</mo> <msub> <mi>Y</mi> <mi>i</mi> </msub> <mo>&lt;</mo> <msubsup> <mi>X</mi> <mi>i</mi> <mo>&amp;prime;</mo> </msubsup> <mi>&amp;beta;</mi> </mrow> </munder> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> <mo>|</mo> <mrow> <msub> <mi>Y</mi> <mi>i</mi> </msub> <mo>-</mo> <msubsup> <mi>X</mi> <mi>i</mi> <mo>&amp;prime;</mo> </msubsup> <mi>&amp;beta;</mi> </mrow> <mo>|</mo> </mrow>
    Some quantile α is given, passes through parameter vector estimate corresponding to solution, you can describe independent variable now to dependent variable Influence；Then when α is in the continuous value in (0,1) feasible section, you can obtain Y condition distribution.
  6. 6. the short-term wind-electricity power probability density Forecasting Methodology of EWT quantile estimates forest according to claim 1, it is special Sign is：Step (5) establishes quantile estimate forest model to each component, obtains different quantile regression forecasting results；It is described The specific calculating process of quantile estimate forest is：
    6.1 random forests are counted as an adaptability nearest neighbour classification and regression process, to each X=x, can obtain original One weight set w of n observed valuei(x), i=1,2, L, n；Random forest essence is added using all dependent variable observations Power and the estimation as dependent variable Y conditional means E (Y | X=x)；In addition, QRF decision trees are produced with standard RF algorithms, condition Distribution is obtained by the dependent variable Weighted estimation observed, wherein the weight of each observation is equal to RF algorithm weights；
    6.2 thus, and QRF defines E (1{Y≤y}| X=x) be estimated as observation 1{Y≤y}Weighted average, i.e.,
    <mrow> <mover> <mi>F</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>y</mi> <mo>|</mo> <mi>X</mi> <mo>=</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>w</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <msub> <mn>1</mn> <mrow> <mo>{</mo> <mi>Y</mi> <mo>&amp;le;</mo> <mi>y</mi> <mo>}</mo> </mrow> </msub> </mrow>
    6.3 k decision tree T (θ of generationt), t=1,2, L, k；To each leaf node of every decision tree, all sights of the leaf node are investigated Measured value；
    6.4 given X=x, travel through all decision trees；Calculate the weight w of every decision tree observationi(x,θt), i ∈ 1,2, L, n}；By to decision tree weight wi(x,θt), t=1,2, L, k are averaged to obtain the weight w of each observation i ∈ { 1,2, L, n }i (x)；
    6.5 couples of all y ∈ R, the weight drawn using step 6.4, you can calculate the estimation of distribution function；To every decision tree Each node, RF, which is returned, only to be retained the average of observation and have ignored other information, and QRF retains all observations in node, And condition distribution is calculated on this basis.
  7. 7. the short-term wind-electricity power probability density Forecasting Methodology of EWT quantile estimates forest according to claim 1, it is special Sign is：The prediction of wind power probability density is obtained using Density Estimator in step (7), and by surveying wind power data Verify the validity of the inventive method；The specific calculating process of Density Estimator is：
    Density Estimator is to estimate its density function by the stochastic variable from same unknown distribution function of one group of observation Nonparametric computational methods；If X1,X2,L,XnUnitary continuous population sample is taken from, the population density function f at the x of arbitrfary point (x) Density Estimator is defined as
    <mrow> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mi>h</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>n</mi> <mi>h</mi> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mi>K</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>x</mi> <mo>-</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> </mrow> <mi>h</mi> </mfrac> <mo>)</mo> </mrow> </mrow>
    In formula：K (x) is kernel function, the gaussian kernel function form used herein forH is bandwidth system Number, span are 1.8~2.0.
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CN109085481A (en) * 2018-10-23 2018-12-25 国网江苏省电力有限公司徐州供电分公司 A kind of cable local discharge localization method based on EWT
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CN111612262A (en) * 2020-01-15 2020-09-01 长沙理工大学 Wind power probability prediction method based on quantile regression
CN112183848A (en) * 2020-09-25 2021-01-05 合肥工业大学 Power load probability prediction method based on DWT-SVQR integration
CN112561414A (en) * 2019-09-25 2021-03-26 顺丰科技有限公司 Inventory management method, device and computer readable storage medium
CN112926801A (en) * 2021-03-31 2021-06-08 云南电网有限责任公司 Load curve combined prediction method and device based on quantile regression
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CN113258565A (en) * 2021-05-11 2021-08-13 广东电网有限责任公司韶关供电局 Frequency adjusting method, device, equipment and storage medium
CN113469467A (en) * 2021-09-02 2021-10-01 国能日新科技股份有限公司 Wind power ultra-short term prediction method and device based on band-pass filtering
CN113536584A (en) * 2021-07-23 2021-10-22 河北工业大学 Wind speed reverse generation method based on probability model and multi-time window self-correlation verification
CN114548464A (en) * 2020-11-19 2022-05-27 国网湖南省电力有限公司 Wind power confidence interval prediction method, device and medium based on wavelet transformation
CN115409296A (en) * 2022-11-02 2022-11-29 国网江西省电力有限公司电力科学研究院 Method for predicting net load probability of active power distribution network

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CN108416695B (en) * 2018-02-24 2020-07-07 合肥工业大学 Power load probability density prediction method, system and medium based on deep learning
CN108416695A (en) * 2018-02-24 2018-08-17 合肥工业大学 Electric load probability density prediction technique based on deep learning and system, medium
CN108460501A (en) * 2018-05-10 2018-08-28 湖北工业大学 A kind of wind power station output power predicting method based on built-up pattern
CN108460501B (en) * 2018-05-10 2021-09-14 湖北工业大学 Wind power station output power prediction method based on combined model
CN108846517A (en) * 2018-06-12 2018-11-20 清华大学 A kind of probability short-term electric load prediction integrated approach of quantile
CN108846517B (en) * 2018-06-12 2021-03-16 清华大学 Integration method for predicating quantile probabilistic short-term power load
CN109086793B (en) * 2018-06-27 2021-11-16 东北大学 Abnormity identification method for wind driven generator
CN109086793A (en) * 2018-06-27 2018-12-25 东北大学 A kind of abnormality recognition method of wind-driven generator
CN109101390B (en) * 2018-06-29 2021-08-24 平安科技（深圳）有限公司 Timed task abnormity monitoring method based on Gaussian distribution, electronic device and medium
CN109101390A (en) * 2018-06-29 2018-12-28 平安科技（深圳）有限公司 Timed task abnormality monitoring method, electronic device and medium based on Gaussian Profile
CN109117992B (en) * 2018-07-27 2022-01-04 华北电力大学 Ultra-short-term wind power prediction method based on WD-LA-WRF model
CN109117992A (en) * 2018-07-27 2019-01-01 华北电力大学 Ultra-short term wind power prediction method based on WD-LA-WRF model
CN108984797A (en) * 2018-08-20 2018-12-11 新疆工程学院 A kind of method for quick estimating of magnanimity monitor-type long-term sequence data related coefficient
CN109085481B (en) * 2018-10-23 2021-11-26 国网江苏省电力有限公司徐州供电分公司 Cable partial discharge positioning method based on EWT
CN109085481A (en) * 2018-10-23 2018-12-25 国网江苏省电力有限公司徐州供电分公司 A kind of cable local discharge localization method based on EWT
CN109597967B (en) * 2018-11-20 2023-08-25 江苏云上电力科技有限公司 Power system distribution substation load data anomaly detection and repair method
CN109597967A (en) * 2018-11-20 2019-04-09 江苏云上电力科技有限公司 A kind of electric system distribution transforming power station load data abnormality detection and restorative procedure
CN112561414A (en) * 2019-09-25 2021-03-26 顺丰科技有限公司 Inventory management method, device and computer readable storage medium
CN110796303B (en) * 2019-10-24 2023-11-07 国网安徽省电力有限公司电力科学研究院 Short-term power load prediction method based on EWT and ODBSCAN
CN110796303A (en) * 2019-10-24 2020-02-14 国网安徽省电力有限公司电力科学研究院 Short-term power load prediction method based on EWT and ODBSCAN
CN111612262A (en) * 2020-01-15 2020-09-01 长沙理工大学 Wind power probability prediction method based on quantile regression
CN112183848B (en) * 2020-09-25 2022-08-30 合肥工业大学 Power load probability prediction method based on DWT-SVQR integration
CN112183848A (en) * 2020-09-25 2021-01-05 合肥工业大学 Power load probability prediction method based on DWT-SVQR integration
CN114548464A (en) * 2020-11-19 2022-05-27 国网湖南省电力有限公司 Wind power confidence interval prediction method, device and medium based on wavelet transformation
CN112926801A (en) * 2021-03-31 2021-06-08 云南电网有限责任公司 Load curve combined prediction method and device based on quantile regression
CN112926801B (en) * 2021-03-31 2022-11-01 云南电网有限责任公司 Load curve combined prediction method and device based on quantile regression
CN113258565A (en) * 2021-05-11 2021-08-13 广东电网有限责任公司韶关供电局 Frequency adjusting method, device, equipment and storage medium
CN113205223A (en) * 2021-05-17 2021-08-03 上海电力大学 Electric quantity prediction system and prediction method thereof
CN113536584A (en) * 2021-07-23 2021-10-22 河北工业大学 Wind speed reverse generation method based on probability model and multi-time window self-correlation verification
CN113469467B (en) * 2021-09-02 2021-11-30 国能日新科技股份有限公司 Wind power ultra-short term prediction method and device based on band-pass filtering
CN113469467A (en) * 2021-09-02 2021-10-01 国能日新科技股份有限公司 Wind power ultra-short term prediction method and device based on band-pass filtering
CN115409296A (en) * 2022-11-02 2022-11-29 国网江西省电力有限公司电力科学研究院 Method for predicting net load probability of active power distribution network

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Application publication date: 20180216